Question

So sánh

a, 6+\(2\sqrt{2}\) và 9

b, \(\sqrt{11}-\sqrt{3}\) và 2

Answer 1

\(a,2\sqrt{2}=\sqrt{8}< \sqrt{9}=3\\ \Leftrightarrow6+2\sqrt{2}< 3+6=9\\ b,\left(\sqrt{11}-\sqrt{3}\right)^2=14-2\sqrt{33}\\ 2^2=4=14-10\\ \left(2\sqrt{33}\right)^2=132>100=10^2\Leftrightarrow-2\sqrt{33}< -10\\ \Leftrightarrow\sqrt{11}-\sqrt{3}< 2\)

Answer 2

a: \(2\sqrt{2}< 3\)

nên \(6+2\sqrt{2}< 9\)